Answer: The required set of pairs is {(1, 1), (2, 3), (3, 3), (4, 3)}.
Step-by-step explanation: We are the set A = {1, 2, 3, 4} and S, R are relations on A , defined as follows :
S = {(1, 1), (1, 3), (2, 3), (3, 4), (4,1)}
R = {(1, 4), (2, 2), (3, 2), (4, 2)}.
We are to write the set of pairs in
S ο R.
We know that for any element x in R, we get
S ο R(x) = S(R(x)).
From the given relations, we have
S ο R(1) = S(R(1)) = S(4) = 1, so the pair is (1, 1).
S ο R(2) = S(R(2)) = S(2) = 3, so the pair is (2, 3).
S ο R(3) = S(R(3)) = S(2) = 3, so the pair is (3, 3).
S ο R(4) = S(R(4)) = S(2) = 3, so the pair is (4, 3).
Thus, the required set of pairs is {(1, 1), (2, 3), (3, 3), (4, 3)}.
